MELJUN CORTES Research Seminar 1 Sampling Theory and Methods

8/17/2019 MELJUN CORTES Research Seminar 1 Sampling Theory and Methods

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Sampling Theory and

MethodsLesson 1

Basics of Sampling Theory


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Sampling

• Very important part of the research process.

• Concerned with selecting a relatively small

number of elements sample! from a largergroup of elements population!.

• "ften used in a survey research when it is

di#cult or impossible to conduct a censuswhere data are gathered from everyelement of the population.


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S$M%L&'( T)*M&'"L"(&)S

Population

•$ set of elements usually grouped e.g.

people+ organi,ations! from which datapertinent to a problem may be collected.

•-ened target population / consists ofelements identied as 0ey informantsessential for investigation based on thelimitations of the research proect.


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S$M%L&'( T)*M&'"L"(&)S

Sample

•

Synonymous to an element of thepopulation

•$ person or obect from which data

are collected and information isderived.


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S$M%L&'( T)*M&'"L"(&)S

Sampling units

•)lements of the target population available

for selection during the sampling process

Sampling Distribution

• Theoretical concept referring to thefre2uency distribution of a specic samplestatistics.


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S$M%L&'( T)*M&'"L"(&)S

Sampling Error

•

$ny type of bias that results frommista0es either in the determination ofthe sample si,e or in the utili,ation ofthe sampling techni2ue or method.


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S$M%L&'( T)*M&'"L"(&)S

Confdence Interval (Margin o Error)

•Statistical range of values within which

the true value of the target populationparameter is e3pected to lie.

•

&t determines how much higher or lowerthan the population mean you are willingto let your sample fall.


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S$M%L&'( T)*M&'"L"(&)S

Confdence Level

•4ow condent do you want to be that theactual mean falls within your condenceinterval5

•Most common condence intervals 678condent+ 698 condent+ and 668condent.


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S$M%L&'( T)*M&'"L"(&)S

Central Limit Teorem

•:or almost all target populations+ the samplingdistributions of the means or the percentage valuederived from a simple random sample will beappro3imately be normally distributed providedthat the sample si,e is su#ciently large. 4air+;77

• The probability is high when the mean of anysample ta0en from the target population closelyapproach as one increases the si,e of the sample.


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S$M%L&'( T)*M&'"L"(&)S

Standard Deviation

•

Variance e3pected in responses

•=se 7.9+ a safe decision and ensures

that the sample will be large enough


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S&>)-)T)*M&'$T&"'

• :actors that determine sample si,e are? – 'ature of data and data analysis – @ind and number of comparisons –

'umber of variables to be investigated – -esired degree of accuracy – 4omogeneity of samples

• -etermining Sample si,e for? – =n0nown population – @nown population


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S&>)-)T)*M&'$T&"'

• Condence level corresponds to a >Ascore+ aconstant value needed for the e2uation.

• >Ascores for the most common condence levels? – 78 A >Ascore !"#$! – 678 A >Ascore !"%&' – 698 A >Ascore !"% – 6D8 A >Ascore #"!

• :or other valueshttp?EEwww.utdallas.eduEdeptEabpE,scoretable.pdf!


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S&>)-)T)*M&'$T&"'

• Sample si,es as small as F7 aregenerally ade2uate to ensure that thesampling distribution of the mean will

appro3imate the normal curve Shott+1667 as cited in Cristobal+ ;71F!

• Ghen the total population is e2ual to orless than 177+ this same number mayserve as the sample si,e universalsampling!.


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:"*M=L$=n0nown %opulation Si,e

• =sed in determining sample si,esfrom un0nown population

'ecessary Sample Si,e

(*+score)# , StdDev , (! - StdDev) .(margin o error)#

Sample si,e 7.;9 desired certainty Eacceptable error! ;


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)3ample 1

• $ssuming you chose 698 condence level+ 7.9standard deviation+ and a margin of errorcondence interval! of HEA 98. 4ow manyrespondents are needed5

recall? 'ecessary Sample Si,e (*+score)# , StdDev , (! - StdDev) . (margin oerror)#

1.6


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)3ample ;

• &f a survey of a group of teachers re2uiresa condence level of 698 and 9 8acceptable error+ then the researcherneeds a sample si,e of FJ teachers that

will have to be surveyed.

:or 698 certainty+ use 1.6<

7.;9 1.6< E 7.79!; 5

7.;9 1+9F


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)3ample F

• &f a researcher wants to e3amine agroup of students with 6D8 certainty+then.

:or 6D8 certainty+ use ;.1D

7.;9 ;.1D E 7.7F!; 57.;9 9+;F;.111! 5

1+F7 students 5


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)3ercise

• $ssume you wish to randomly sampleteachers across the southeast =S$.Gith a 678 condence level+ what

sample si,e would be needed5

7.;9 1.


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)3ercise

• Kou wish to estimate the proportion ofall buyers that are young buyers with698 condence. 4ow many

observations are needed to estimate thepopulation proportion within 7.7< error5

– $ssuming that nothing is 0nown about thepopulation proportion.

– $ssuming that the population proportion hasrecently been estimated to be 7.FJ.


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)3ercise

– $ssuming that nothing is 0nown aboutthe population proportion.

1.6

F.J1< I 7.;9! E7.77F<

7.6


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)3ercise

– $ssuming that the population proportion hasrecently been estimated to be 7.FJ.

Since a prior estimate of the population

proportion is known (0.34), use it as thestandard deviation.

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F.J1

7.


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:"*M=L$@nown %opulation Si,e

• =se of Slovins :ormula used to calculate anappropriate sample si,e from a population!.

n = N / (1 + Ne2 )

Ghere?n sample si,e' populatione estimate of error acceptable error!

I The error tolerance+ e+ can be given in a2uestion! or if you want to gure it out onyour own+ ust subtract the condence levelfrom 1.


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)3ample 1

• )stimate the sample si,e from apopulation of 9777 freshmen studentsusing 98 acceptable error.

n ' E 1H 'e;!

9777 E 1 H 9777!7.79!;!

9777 E 1 H 1;.9! 9777 E 1F.9

FD7 students


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)3ample 1

• )stimate the sample si,e from apopulation of 9777 freshmen studentsusing 98 acceptable error.

n ' E 1H 'e;!

9777 E 1 H 9777!7.79!;!

9777 E 1 H 1;.9! 9777 E 1F.9

FD7 students


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)3ercise

• $ researcher plans to conduct a survey. &fthe population on Smith City is 1+777+777nd the sample si,e if the margin of error is198

n ' E 1H 'e;!

1+777+777 E 1 H 1+777+777!7.19!;! 1+777+777 E 1 H 1+777+777!7.7;;9!! 1+777+777 E 1 H ;;+977!

1+777+777 E ;;+971 J9 people rounded up!


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S/MPLI01 T2E345 /0DMET23DS

Lesson ;

Sampling Methods


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The %roblem

• Suppose a school would li0e todetermine the wee0ly foode3penditure of its students+ if there

are 1+777 students and the guidancecounselor decided to use only 177students as a sample+ who will be

included in the sample5


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Sampling Method

• Sampling Method or Sampling Techni2ueis the process of determining or selectingthose sample units which would providethe re2uired estimates with associatedmargins of error+ arising from e3aminingonly a part and not the whole.

•

Two methods are used? probabilitysampling and nonAprobability sampling.


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Sampling MethodSampling Tecni6ue

%robabilitySampling

Simple *andom Sampling

Systematic *andom

SamplingStratied *andomSamplingCluster Sampling

MultiAstage Sampling

'onA%robabilitySampling

Convenience Sampling

uota Sampling

%urposive Sampling


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%robability Sampling

• )ach eligible member of the populationhas a specic and 0nown chance ofbeing included in the sample.

• $lso termed as scientic sampling.

•

Ghen using this techni2ue+ it isimportant to have a complete list ofthe members of the population.


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%robability SamplingSimple *andom Sampling

• Lottery method

– Grite names or codes on a piece ofpaper

– %ut in a container

– *andomly select the desired number ofsamples

• :ishbowl techni2ue


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%robability SamplingSystematic *andom Sampling

• Choose a starting point then select everyk th element of the population using k = N /n.

• )3. The town of :airfa3 is divided up into9D< bloc0s which are numberedconsecutively. $ 17 percent sample bloc0s

is to be ta0en for the study. &f the randomnumber chosen between 1 to 0 is F+ whatare the bloc0s considered for the sample5


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%robability SamplingSystematic *andom Sampling

• Solution? – -etermine 0N k = !" # $0 percent of !"

= !" # !." = $0

this means %ou have to include ever% $0th mem&er of the population after choosing arandom start.

– *andom number F can be determined

via the lottery method! – Bloc0s considered for the ample are? 7F+

1F+ ;F+ FF+ JF+ O+ 9DF


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%robability SamplingStratied *andom Sampling

• %opulation is subdivided into at leasttwo diPerent subpopulations orstrata! that share the same

characteristics such as gender+ age!.Samples are derived from these

strata using the other sampling

techni2ues.


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• )3. $ssuming a barangay of 17+777families belonging to diPerentincome brac0ets+ a survey to nd out

how many are in favor of the *4 billis to be conducted. To ensure that allincome groups are represented+

respondents will be divided into 4ighA&ncome+ $verageA&ncome+ and LowA&ncome.


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Strata 0umber o amilies

4igh / &ncome ;+777

$verage / &ncome 9+777

Low / &ncome F+777

' 17+777


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• =sing a 98 margin of error+ howmany families should be included inthe sample5

•

=sing either proportional or e2ualallocation+ how many from eachgroup should be ta0en as samples5


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• =sing a 98 margin of error+ how manyfamilies should be included in the sample5

n 17+777 E 1 H 17+777!7.79!; !

n 17+777 E 1 H 17+777!7.77;9!

n 17+777 E 1 H ;9!

n 17+777 E ;<

n F9 families rounded up!


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• =sing either proportional or e2ualallocation+ how many from eachgroup should be ta0en as samples5


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Strata0umber o

amiliesPercent

Proportional

E6ual

4igh /&ncome ;+777

;+777 E17+777 7.;7 or

;78

7.;F9! DD

F9EF 1;

$verage /&ncome 9+777

9+777 E17+777

7.97 or978

7.9F9!

16F1;6

Low /&ncome F+777

F+777 E17+777 7.F7 or

F78

7.FF9! 119

1;

' 17+777

1778 F9 F9


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%robability SamplingCluster Sampling

• 'ormally used in largeAscale studies inwhich the population is geographicallyspread out where sampling procedures may

be di#cult and time consuming.

• %rocess?

– -ivide the population area into sections or

clusters! – Then randomly select a few of those sections

– *andomly select a sample from those sections


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%robability SamplingCluster Sampling

• )3. Suppose we want to determinethe average daily e3penses offamilies in the City of Santa *osa.

Ge can draw a random sample of 9barangays from the total 19 usingrandom sampling and then get a

certain number of families from eachof the 9 barangays.


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%robability SamplingMultiAStage Sampling

• Combination of several samplingtechni2ues discussed


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'onA%robability Sampling

• Members of the sample si,e are drawnbased on the udgment of the researcher.

•&t is a process of selection in which not allmembers of the entire population aregiven a chance of being selected assamples.

• Sometimes referred to as su&'ectivesampling or nonscientic sampling.


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'onA%robability SamplingConvenience Sampling

• Simply use results that are readilyavailable.

• $lso called accidental or incidental sampling.


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'onA%robability Samplinguota Sampling

• Similar to stratied sampling in whichthe researcher rst identies thestrata and their proportions as they

are represented in the population.

• Convenience or udgment sampling is

used to select the re2uired numberof subects from each stratum.


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'onA%robability Sampling%urposive Sampling

• 4andpic0ing of subectsN also called 'udgmental sampling

•

Selects members or elements based on theparticular purpose of the e3periment orstudy.

•

=seful for situations where you need to reacha targeted sample 2uic0ly and wheresampling for proportionality is not theprimary concern.


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The %roblem

• Suppose a school would li0e to determine thewee0ly food e3penditure of its students+ ifthere are 1+777 students and the guidancecounselor decided to use only 177 studentsas a sample+ who will be included in thesample5

•

7ind a partner and elp te scool decide on8ic sampling tecni6ue sould te9 use inselecting students or te sample" Presenttree (:) coices"


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)3ercise

• &dentify which sampling techni2ue wasused in the following scenarios?

1. Ghen she wrote omen and *moticons+

author @C %ascual based conclusions on J+977responses from 177+777 2uestionnairesdistributed to women.

;. The (uidance Counselor of a high schoolsurveys all students from each of the ;7randomly selected classes.

F. $ sociologist at selects 19 men and 19 womenfrom each of J Math classes.


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)3ercise

• &dentify which sampling techni2ue wasused in the following scenarios contd!?

J. &BM selects ;77th compact dis0 from theassembly line and conducts a thorough test of2uality

9. The court secretary writes the name of eachMunicipal Qudge on a separate card+ shuResthe cards+ and then draws F names.


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)3ercise

• &dentify which sampling techni2ue wasused in the following scenarios contd!?D. The mar0eting manager of ebay.ph tests a

new sales strategy by randomly selecting197 consumers with less than %177+777 ingross income and 197 consumers withgross income of at least %177+777.

. $ mar0et researcher for Champion-etergent interviews all passengers oneach of 17 randomly selected %=Vs.


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)3ercise

• &dentify which sampling techni2ue wasused in the following scenarioscontd!?

6. $ medical researcher from =nilever %hils.interviews all leu0emia patients in eachof ;7 randomly selected hospitals.

17.&n conducting research for the eveningnews+ a reporter for $BSACB' interviews19 people as they leave a shopping mall.


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)3ercise

• Solve the following?

– $ researcher would li0e to investigatethe perception of students on

mathematics. 4e divided the populationinto subApopulations as shown in thetable. =se stratied random sampling ifthe sample to be drawn consists of 977

students.


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)3ercise

Strata 0umber o Students

:irst year 1

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MELJUN CORTES Research Seminar 1 Sampling Theory and Methods